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Application of the Level Method for Computing Locational Convex Hull Prices

Author

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  • Stevens, Nicolas

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Papavasiliou, Anthony

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

Convex hull pricing is a well-documented method for coping with the non-existence of uniform clearing prices in electricity markets with non-convex costs and constraints. We revisit primal and dual methods for computing convex hull prices, and discuss the positioning of existing approximation methods in this taxonomy. We propose a dual decomposition algorithm known as the Level Method and we adapt the basic algorithm to the specificities of convex hull pricing. We benchmark its performance against a column generation algorithm that has recently been proposed in the literature. We provide empirical evidence about the favorable performance of our algorithm on large test instances based on PJM and Central Europe.

Suggested Citation

  • Stevens, Nicolas & Papavasiliou, Anthony, 2022. "Application of the Level Method for Computing Locational Convex Hull Prices," LIDAM Discussion Papers CORE 2022002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2022002
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    References listed on IDEAS

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    1. VAN VYVE, Mathieu, 2011. "Linear prices for non-convex electricity markets: models and algorithms," LIDAM Discussion Papers CORE 2011050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Nikolaus Wollscheid & J. Luis Pérez Lustres & Oskar Kefer & Sebastian Hahn & Victor Brosius & Uwe H. F. Bunz & Marcus Motzkus & Tiago Buckup, 2019. "Oxygen-catalysed sequential singlet fission," Nature Communications, Nature, vol. 10(1), pages 1-7, December.
    3. Roger E. Bohn & Michael C. Caramanis & Fred C. Schweppe, 1984. "Optimal Pricing in Electrical Networks over Space and Time," RAND Journal of Economics, The RAND Corporation, vol. 15(3), pages 360-376, Autumn.
    4. Bernard Knueven & James Ostrowski & Jean-Paul Watson, 2020. "On Mixed-Integer Programming Formulations for the Unit Commitment Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 857-876, October.
    5. Christoph Schnedermann & Antonios M. Alvertis & Torsten Wende & Steven Lukman & Jiaqi Feng & Florian A. Y. N. Schröder & David H. P. Turban & Jishan Wu & Nicholas D. M. Hine & Neil C. Greenham & Alex , 2019. "A molecular movie of ultrafast singlet fission," Nature Communications, Nature, vol. 10(1), pages 1-11, December.
    6. Dai-Van Vo & Minh-Khai Nguyen & Duc-Tri Do & Youn-Ok Choi, 2019. "A Single-Phase Nine-Level Boost Inverter," Energies, MDPI, vol. 12(3), pages 1-14, January.
    7. Queyranne, M. & Wolsey, L.A., 2015. "Tight MIP Formulations for Bounded Up/Down Times and Interval-Dependent Start-Ups," LIDAM Discussion Papers CORE 2015036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Gert-Jan Hendriks & Lisa A. Jung & Anton J. M. Larsson & Michael Lidschreiber & Oscar Andersson Forsman & Katja Lidschreiber & Patrick Cramer & Rickard Sandberg, 2019. "NASC-seq monitors RNA synthesis in single cells," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    9. Panagiotis Andrianesis & Dimitris Bertsimas & Michael C. Caramanis & William W. Hogan, 2020. "Computation of Convex Hull Prices in Electricity Markets with Non-Convexities using Dantzig-Wolfe Decomposition," Papers 2012.13331, arXiv.org, revised Oct 2021.
    10. Wentao Gan & Chaoji Chen & Hyun-Tae Kim & Zhiwei Lin & Jiaqi Dai & Zhihua Dong & Zhan Zhou & Weiwei Ping & Shuaiming He & Shaoliang Xiao & Miao Yu & Liangbing Hu, 2019. "Single-digit-micrometer thickness wood speaker," Nature Communications, Nature, vol. 10(1), pages 1-8, December.
    11. Birge, John R. & Louveaux, Francois V., 1988. "A multicut algorithm for two-stage stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 34(3), pages 384-392, March.
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    Keywords

    Convex hull pricing ; Non-uniform pricing ; Level method ; Bundle methods;
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